Finite Group Databasebeta

← #15833872

Subgroups — #15833872

Order 3328.

616 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13124848C211yesmaximal, characteristic
2#13123853C211yesmaximal, characteristic, complemented
3#13123841C211yesmaximal, characteristic, complemented
4#13113723C211yesmaximal, characteristic, complemented
5#13113718C211yesmaximal, characteristic, complemented
6#13113689C211yesmaximal, characteristic, complemented
7#13113682C211yesmaximal, characteristic, complemented
8#13113676C211yesmaximal, characteristic, complemented
9#13113662C211yesmaximal, characteristic, complemented
10#13113640C211yesmaximal, characteristic, complemented
11#13113639C211yesmaximal, characteristic, complemented
12#13113617C211yesmaximal, characteristic, complemented
13#13113219C211yesmaximal, characteristic, complemented
14C8×#6099C211yesmaximal, characteristic, complemented
15C13×#1494C211yesmaximal, characteristic, complemented
16C13×#529C2211yescharacteristic
17C4×#6127C2211yescharacteristic
18C13×#432C2211yescharacteristic
19C2×C4×C8×C13C2211yescharacteristic
20#11718727C411yescharacteristic
21#11718724C411yescharacteristic
22#11718718C411yescharacteristic
23#11718715C411yescharacteristic
24#11718708C411yescharacteristic
25#11718706C411yescharacteristic
26#11718698C411yescharacteristic
27#11718696C411yescharacteristic
28C4×#6107C2211yescharacteristic
29C4×#6106C2211yescharacteristic
30#11718685C2211yescharacteristic
31Q8×#1055C2211yescharacteristic
32C4×#6105C2211yescharacteristic
33C4×#6104C2211yescharacteristic
34#11718673—21no—
35#11718673C2211yescharacteristic
36#11718672—21no—
37D4×#1055C2211yescharacteristic
38#11718661—21no—
39#11718658—21no—
40#11718586C2211yescharacteristic
41#11718586C2211yescharacteristic
42C4×#6099C2211yescharacteristic
43#11718499C2211yescharacteristic
44#11718499C2211yescharacteristic
45#11718491C2211yescharacteristic
46#11718491C2211yescharacteristic
47#11718390—21no—
48#11718390—21no—
49#11718368—21no—
50#11718366—21no—
51C13×Q8⋊C8C2211yescharacteristic
52C13×Q8⋊C8C2211yescharacteristic
53C13×D4⋊C8C2211yescharacteristic
54C13×D4⋊C8C2211yescharacteristic
55#11718072C2211yescharacteristic
56#11718072C2211yescharacteristic
57#11718071C2211yescharacteristic
58#11718071C2211yescharacteristic
59#11718051C2211yescharacteristic
60#11718051C2211yescharacteristic
61#11718048C2211yescharacteristic
62#11718048C2211yescharacteristic
63#11718046C2211yescharacteristic
64#11718046C2211yescharacteristic
65C8×#1055C2211yescharacteristic
66C8×#1055C2211yescharacteristic
67C2×#6127C2×C411yescharacteristic
68C22×C8×C13—21no—
69C13×#126—21no—
70C13×#125C2×C411yescharacteristic
71C13×#124C2×C411yescharacteristic
72C13×#123—21no—
73C13×C22⋊Q8C2×C411yescharacteristic
74C13×#121C2×C411yescharacteristic
75C4×Q8×C13C2311yescharacteristic
76C4×D4×C13—21no—
77C4×D4×C13C2311yescharacteristic
78C13×#117—21no—
79C2×C42×C13C2311yescharacteristic
80C2×#6107C2×C411yescharacteristic
81C2×#6106C2×C411yescharacteristic
82C2×#6105C2×C411yescharacteristic
83C2×#6104C2×C411yescharacteristic
84C4×C22⋊D13—21no—
85C4×C22⋊D13—21no—
86#88180C2×C411yescharacteristic
87C2×#6099—21no—
88C2×#6099D411yescharacteristic
89C2×#6099D411yescharacteristic
90C22×#1055—21no—
91C2×#6094—21no—
92C2×#6094—21no—
93C4×D52C2×C411yescharacteristic
94C4×D52C2311yescharacteristic
95#88126—21no—
96C42×D13—21no—
97C4×Dic26C2×C411yescharacteristic
98C4×Dic26C2311yescharacteristic
99C13×C4⋊C8C2311yescharacteristic
100C13×C4⋊C8C2311yescharacteristic
101C13×C22⋊C8—21no—
102C13×#97—21no—
103C4×C8×C13—21no—
104C4×C8×C13C2311yescharacteristic
105C4×C8×C13C2311yescharacteristic
106#88075C2×C411yescharacteristic
107#88075C2×C411yescharacteristic
108#88072C2×C411yescharacteristic
109#88072C2×C411yescharacteristic
110C22⋊#1055—21no—
111C22⋊#1055—21no—
112C22⋊#1055—21no—
113C22⋊#1055C2×C411yescharacteristic
114C22⋊#1055C2×C411yescharacteristic
115#88060—21no—
116#88060—21no—
117#88054—21no—
118#88054—21no—
119C8×Dic13—21no—
120C8×Dic13—21no—
121#88050C2×C411yescharacteristic
122#88050C2×C411yescharacteristic
123#88049C2×C411yescharacteristic
124#88049C2×C411yescharacteristic
125#88048C2×C411yescharacteristic
126#88048C2×C411yescharacteristic
127#88047C2×C411yescharacteristic
128#88047C2×C411yescharacteristic
129C4⋊#1055—21no—
130C4⋊#1055—21no—
131C4⋊#1055C2×C411yescharacteristic
132C4⋊#1055C2×C411yescharacteristic
133C4⋊#1055C2311yescharacteristic
134C4⋊#1055C2311yescharacteristic
135#88043—21no—
136#88043D411yescharacteristic
137#88043D411yescharacteristic
138C4×#1055—21no—
139C4×#1055—21no—
140C4×#1055C2311yescharacteristic
141C4×#1055C2311yescharacteristic
142C4×#1055C2311yescharacteristic
143C4×#1055C2311yescharacteristic
144#17999—131nomaximal, Sylow
145C2×Q8×C13C22×C411yescharacteristic
146C2×D4×C13—21no—
147C2×D4×C13C22×C411yescharacteristic
148C22×C4×C13—21no—
149C22×C4×C13C22×C411yescharacteristic
150C22×C4×C13C2×D411yescharacteristic
151C22×C4×C13#4111yescharacteristic
152C2×C22⋊D13—21no—
153#6127—22no—
154#6127—41no—
155C2×D52C22×C411yescharacteristic
156C2×C4×D13—21no—
157C2×C4×D13—21no—
158C2×C4×D13—21no—
159C2×Dic26C22×C411yescharacteristic
160C2×C8×C13—21no—
161C2×C8×C13—21no—
162C2×C8×C13—21no—
163C2×C8×C13—21no—
164C2×C8×C13—42no—
165C13×C4⋊C4—21no—
166C13×C4⋊C4—21no—
167C13×C4⋊C4—21no—
168C13×C4⋊C4—21no—
169C13×C4⋊C4C22×C411yescharacteristic
170C13×C4⋊C4C22×C411yescharacteristic
171C13×C22⋊C4—21no—
172C13×C22⋊C4—21no—
173C13×C22⋊C4—21no—
174C13×C22⋊C4—21no—
175C13×C22⋊C4—21no—
176C42×C13—21no—
177C42×C13C22×C411yescharacteristic
178C42×C13C2×D411yescharacteristic
179C42×C13#4111yescharacteristic
180C42×C13C2411yescharacteristic
181C22⋊Dic13—21no—
182#6107—22no—
183#6106—41no—
184#6105—22no—
185#6104—41no—
186#6103—21no—
187#6103—21no—
188C4⋊Dic13C22×C411yescharacteristic
189C4⋊Dic13C22×C411yescharacteristic
190#6101—21no—
191#6101—21no—
192C4×Dic13—21no—
193C4×Dic13—21no—
194C4×Dic13—21no—
195#6099—22no—
196#6099—22no—
197#6099—42no—
198C2×#1055—21no—
199C2×#1055—21no—
200C2×#1055—42no—
201C2×#1055C22×C411yescharacteristic
202C2×#1055C22×C411yescharacteristic
203C2×#1055C22×C411yescharacteristic
204C2×#1055C22×C411yescharacteristic
205C2×#1055C2×D411yescharacteristic
206C2×#1055C2×D411yescharacteristic
207C2×#1055C2×D411yescharacteristic
208C2×#1055C2×D411yescharacteristic
209#6094—42no—
210#6094—42no—
211#3102—131no—
212#2971—131no—
213#2969—131no—
214#1590—131no—
215#1589—131no—
216#1584—131no—
217#1583—131no—
218#1583—131no—
219#1581—131no—
220C8×Q16—131no—
221C8×SD16—131no—
222#1572—131no—
223#1494D1311yescharacteristic, complemented
224#1476—131no—
225C8×M16—131no—
226C23×C13—21no—
227C23×C13C4×D411yescharacteristic
228C22×D13—21no—
229Q8×C13—21no—
230Q8×C13—21no—
231D4×C13—21no—
232D4×C13—21no—
233D4×C13—81no—
234C2×C4×C13—21no—
235C2×C4×C13—21no—
236C2×C4×C13—21no—
237C2×C4×C13—21no—
238C2×C4×C13—21no—
239C2×C4×C13—21no—
240C2×C4×C13—21no—
241C2×C4×C13—41no—
242C2×C4×C13—41no—
243C2×C4×C13—41no—
244C2×C4×C13C4×D411yescharacteristic
245C2×C4×C13C4×D411yescharacteristic
246C2×C4×C13C4×D411yescharacteristic
247C2×C4×C13C23×C411yescharacteristic
248C2×C4×C13C22×D411yescharacteristic
249C2×C4×C13C2×#4111yescharacteristic
250C22⋊D13—42no—
251C2×Dic13—21no—
252C2×Dic13—21no—
253C2×Dic13—21no—
254D52—21no—
255D52—21no—
256C4×D13—42no—
257C4×D13—41no—
258C4×D13—41no—
259C4×D13—81no—
260Dic26—21no—
261Dic26#13112yes—
262C8×C13—22no—
263C8×C13—41no—
264C8×C13—41no—
265C8×C13—41no—
266#1055—21no—
267#1055—21no—
268#1055—21no—
269#1055—21no—
270#1055—21no—
271#1055—21no—
272#1055—41no—
273#1055—41no—
274#1055#13512yes—
275#1055#13512yes—
276#529C2×D1311yescharacteristic
277C4×#41—131no—
278#485—131no—
279#482—131no—
280#479—131no—
281#478—131no—
282#464—131no—
283#463—131no—
284#452—131no—
285#449—131no—
286#446—131no—
287C8×Q8—131no—
288C8×Q8—131no—
289C8×Q8—131no—
290C4×Q16—131no—
291C4×SD16—131no—
292C4×SD16—131no—
293C4×D8—131no—
294#436—131no—
295#436—131no—
296#436—131no—
297#436—261no—
298#436—261no—
299#436—261no—
300#435—261no—
301C8×D4—131no—
302#433—261no—
303#432—261no—
304#432C2×D1311yescharacteristic
305#431—131no—
306#431—131no—
307#405—261no—
308C4×M16—131no—
309C4×M16—261no—
310C2×C4×C8C2×D1311yescharacteristic
311#335—131no—
312#335—131no—
313#334—131no—
314#334—131no—
315Q8⋊C8—131no—
316Q8⋊C8—131no—
317Q8⋊C8C2×D1311yescharacteristic
318Q8⋊C8C2×D1311yescharacteristic
319D4⋊C8—131no—
320D4⋊C8—131no—
321D4⋊C8C2×D1311yescharacteristic
322D4⋊C8C2×D1311yescharacteristic
323#322—131no—
324#322—131no—
325C82—131no—
326C82—131no—
327C22×C13—21no—
328C22×C13—21no—
329C22×C13—21no—
330C22×C13—41no—
331C22×C13—41no—
332C22×C13—41no—
333C22×C13C2×C4×D411yescharacteristic
334C2×D13—41no—
335C2×D13—41no—
336C2×D13—41no—
337C4×C13—21no—
338C4×C13—21no—
339C4×C13—21no—
340C4×C13—21no—
341C4×C13—41no—
342C4×C13—41no—
343C4×C13—41no—
344C4×C13C2×#13111yescharacteristic
345C4×C13#56811yescharacteristic
346C4×C13C2×#13511yescharacteristic
347C4×C13C2×#13511yescharacteristic
348Dic13—22no—
349Dic13—41no—
350Dic13—41no—
351C2×#41—131no—
352C2×Q16—131no—
353C2×SD16—131no—
354C2×SD16—131no—
355C2×D8—131no—
356C2×M16—131no—
357C2×M16—131no—
358C2×M16—261no—
359C2×M16—261no—
360C2×M16—261no—
361C22×C8—21no—
362C22×C8—261no—
363#126—21no—
364#125C4×D1311yescharacteristic
365#124C4×D1311yescharacteristic
366#123—21no—
367C22⋊Q8C4×D1311yescharacteristic
368#121C4×D1311yescharacteristic
369C4×Q8—131no—
370C4×Q8—131no—
371C4×Q8C22×D1311yescharacteristic
372C4×D4—21no—
373C4×D4—131no—
374C4×D4—131no—
375C4×D4—261no—
376C4×D4—261no—
377C4×D4C22×D1311yescharacteristic
378#117—21no—
379#117—131no—
380#117—261no—
381C2×C42—261no—
382C2×C42C22×D1311yescharacteristic
383#107—131no—
384#107—131no—
385#106—131no—
386#106—131no—
387C4⋊C8—131no—
388C4⋊C8—131no—
389C4⋊C8—131no—
390C4⋊C8—131no—
391C4⋊C8—261no—
392C4⋊C8—261no—
393C4⋊C8—261no—
394C4⋊C8—261no—
395C4⋊C8C22×D1311yescharacteristic
396C4⋊C8C22×D1311yescharacteristic
397#103—131no—
398#103—131no—
399#103—131no—
400#103—131no—
401#102—131no—
402#102—131no—
403#102—131no—
404#102—131no—
405C22⋊C8—21no—
406C22⋊C8—131no—
407C22⋊C8—131no—
408C22⋊C8—261no—
409C22⋊C8—261no—
410C22⋊C8—261no—
411C22⋊C8—261no—
412C22⋊C8—261no—
413#97—21no—
414#97—131no—
415#97—131no—
416#97—261no—
417C4×C8—21no—
418C4×C8—131no—
419C4×C8—131no—
420C4×C8—131no—
421C4×C8—131no—
422C4×C8—261no—
423C4×C8—261no—
424C4×C8—261no—
425C4×C8—261no—
426C4×C8C22×D1311yescharacteristic
427C4×C8C22×D1311yescharacteristic
428C2×C13—41no—
429C2×C13—81no—
430C2×C13#293311yescharacteristic
431C2×C13C4×#13511yescharacteristic
432C2×C13#295611yescharacteristic
433D13—81no—
434#41—262no—
435#41—521no—
436C2×Q8—131no—
437C2×Q8C2×C4×D1311yescharacteristic
438C2×D4—21no—
439C2×D4—131no—
440C2×D4—261no—
441C2×D4C2×C4×D1311yescharacteristic
442C22×C4—21no—
443C22×C4—261no—
444C22×C4—261no—
445C22×C4—261no—
446C22×C4C2×C4×D1311yescharacteristic
447C22×C4D4×D1311yescharacteristic
448C22×C4#612911yescharacteristic
449Q16—262no—
450SD16—262no—
451SD16—521no—
452D8—521no—
453M16—262no—
454M16—262no—
455M16—522no—
456M16—522no—
457M16—522no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—42no—
463C2×C8—131no—
464C2×C8—131no—
465C2×C8—131no—
466C2×C8—131no—
467C2×C8—131no—
468C2×C8—131no—
469C2×C8—131no—
470C2×C8—131no—
471C2×C8—261no—
472C2×C8—261no—
473C2×C8—522no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—131no—
479C4⋊C4—131no—
480C4⋊C4—261no—
481C4⋊C4—261no—
482C4⋊C4C2×C4×D1311yescharacteristic
483C4⋊C4C2×C4×D1311yescharacteristic
484C22⋊C4—21no—
485C22⋊C4—21no—
486C22⋊C4—21no—
487C22⋊C4—21no—
488C22⋊C4—21no—
489C22⋊C4—261no—
490C22⋊C4—261no—
491C22⋊C4—261no—
492C42—21no—
493C42—261no—
494C42—261no—
495C42—261no—
496C42C2×C4×D1311yescharacteristic
497C42D4×D1311yescharacteristic
498C42#612911yescharacteristic
499C42C23×D1311yescharacteristic
500C13#1799911yescharacteristic, complemented, Sylow
501C23—21no—
502C23—261no—
503C23#8813511yescharacteristic
504Q8—21no—
505Q8—21no—
506Q8—132no—
507Q8—261no—
508D4—21no—
509D4—21no—
510D4—81no—
511D4—261no—
512D4—261no—
513D4—522no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—261no—
525C2×C4—261no—
526C2×C4—261no—
527C2×C4—522no—
528C2×C4—521no—
529C2×C4—521no—
530C2×C4—1041no—
531C2×C4#8813511yescharacteristic
532C2×C4#8813511yescharacteristic
533C2×C4#8813511yescharacteristic
534C2×C4C22×C4×D1311yescharacteristic
535C2×C4C2×D4×D1311yescharacteristic
536C2×C4C2×#612911yescharacteristic
537C8—22no—
538C8—41no—
539C8—41no—
540C8—41no—
541C8—132no—
542C8—132no—
543C8—261no—
544C8—261no—
545C8—261no—
546C8—261no—
547C8—261no—
548C8—261no—
549C8—521no—
550C8—521no—
551C22—21no—
552C22—21no—
553C22—21no—
554C22—41no—
555C22—41no—
556C22—41no—
557C22—521no—
558C22—521no—
559C22—521no—
560C22C2×#8813511yescharacteristic
561C4—21no—
562C4—21no—
563C4—21no—
564C4—21no—
565C4—41no—
566C4—41no—
567C4—41no—
568C4—262no—
569C4—521no—
570C4—521no—
571C4D13×#13111yescharacteristic
572C4#1171945511yescharacteristic
573C4D13×#13511yescharacteristic
574C4D13×#13511yescharacteristic
575C2—41no—
576C2—81no—
577C2—1041no—
578C2#1312356611yescharacteristic
579C2#1312360411yescharacteristic
580C2#1312374211yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC13×#1494C2
socleC22×C13C2×C4×D4
prime radical#11718698C4
cosocleC42×C13C24
hypercenter#1494D13
hypocenterC13#17999
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1494

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #13123853C2semidirect
3. #13123841C2semidirect
4. #13113723C2semidirect
5. #13113718C2semidirect
6. #13113689C2semidirect
7. #13113682C2semidirect
8. #13113676C2semidirect
9. #13113662C2semidirect
10. #13113640C2semidirect
11. #13113639C2semidirect
12. #13113617C2semidirect
13. #13113219C2semidirect
14. C8×#6099C2semidirect
15. C13×#1494C2semidirect
223. #1494D13semidirect
500. C13#17999semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#131248482
#131238532
#131238412
#131137232
#131137182
#131136892
#131136822
#131136762
#131136622
#131136402
#131136392
#131136172
#131132192
C8×#60992
C13×#14942
#1799913